Resistance network



July 8, 1947.

J. R. MOORE 2,423,463

RESISTANCE NETWORK Filed Dec. 28, 1942 'vvvv s JAMES R.MOORE PatentedJuly 8, 1947 RESISTANCE NETWORK James R. Moore, Rumson, N. J., assignorto the United States of America, as represented by the Secretary of WarApplication December 28, 1942, Serial No. 470,413

(Granted under the act of March 3, 1883, as

6 Claims.

The invention described herein may be manufactured and used by or forthe Government for governmental purposes, without the payment to me ofany royalty thereon.

My present invention has to do with resistance networks. Moreparticularly, it relates to a device for adjusting electrical resistancewhereby a voltage is varied in accordance with a predeterminednon-linear mathematical curve.

It is the main object of my present invention to provid a device of thegeneral character indicated wherein a variation of resistance and,therefore, a variation in voltage is made substantially smooth andcontinuous to closely approximate the exponential charging rate of acapacitance.

While not limited thereto, my present invention is admirably adapted tocontrolling the operation of a range-determining device.

In the accompanying specification I describe and in the annexed drawingI show an illustrative embodiment of the resistance network of thepresent invention.

In said drawing, the single figure is a schematic diagram of aresistance network assembled in accordance with .the principles of thepresent invention. I

Referring now more in detail to the present invention, with particularreference to the drawing illustrating a preferred embodiment thereof,the reference character R generally designates a group ofseries-connected resistors R1, R2, R3, R4, Rn. Associated with saidresistors are contacts Re, Re, Rb, Re, Rd, Rim, and selectivelyengageable with said contacts is an adjustable arm 0.

The resistor R1 is connected to one terminal of a source of voltage Eand the arm is connected, through a fixed high resistance Rs, to theother terminal of said source of voltage.

The value of each resistor R1, R2, R3, R4, Rn is such that the voltagedrop across the total resistance of the combination of resistorsrespectively corresponding to each of the contacts Re, Re, Rb, Re, Rd,Rm, is an exponential function of the number of resistors in each suchcombinatlon.

Adjacent the group R of resistors, I provide a second group R" ofseries-connected resistors R'1, R2, R's, R'4, Rn and associated contactsR'o, R's, R's, R'c, R'd, R'm. The resistor R1 is connected to a secondadjustable arm P selectively engageable with the contacts Ra, Ra, Rb,Re, Ed. Rm; and selectively engageable with any of the contacts R'o,R's, R'b, R'c, R's,

amended April 30, 1928; 370 O. G. 757) R'm is a third adjustable arm Q,the opposite end of which is connected with the adjustable arm 0. Thevalue of each resistor R1, Rz, R'a, R4, R'n is such that the equivalentresistance and, therefore, the voltage drop across the parallelcombination of selected resistors R'l, R'z, R's, R4, R'n and anyselected resistor of the group R is an approximately linear function ofthe number of resistors of the group R. entering into the combination.

The output voltage of the network, designated in the drawing as E0, isbetween the contact R0 and the meeting point of the adjustable arms 0and Q.

I shall now describe a specific procedure for determining the values ofthe various resistors above referred to.

The potential across a resistance-capacitance combination builds up inaccordance with the formula:

where A and B are constants depending upon any selected resistance andcapacitance for the circuit under consideration and T is time measuredfrom the instant of application of the potential E.

Now the group R of resistors 15 divided into n sections such that 2 vAE(1 K E for integral values of it up to and including n; and V is theoutput voltage across a selected number of resistors of the group R,excluding the effect of the parallel group R, and k is said selectednumber of resistors.

From Ohms law,

and V =IS Where Sr is the value of the selected number of Solving forSir, We find 3 The value of each resistor R1, R2, R3, R4, can bedetermined from the formula:

(7) R,, =S S,,- Substituting therein for Sr and sir-1, we have ree e ceand substituting still further, for

Fe m Fu and simplifying, we have Hts- )"Htse where k takes on valuesfrom to Thus, having selected values for A, B, and R for the group R,comprising 11 sections of resistors, we can immediately determine fromEquation 9 the value of each of said resistors.

The procedure for calculating the values of the resistors R1, Rz, R's,R's, Rn, of the group R is as follows:

The group R consists of n sections, not necessarily the same number asincluded in the group R, having values such that the equivalentresistance across the parallel combination of RR and S'h is given aswher Sh is the total value of the first h resistors of the n res i storsof the group R, It varies from 0 to n and R. is the average value of theabovedefined Rr. Therefore, by applying the law of parallel circuits, wehave Solving for Sn we obtain The value of each resistor Ri, R2, R's,Ri, Rn can be determined from the formula:

Eliminating I, we obtain as a final expression of the voltage output ofthe entire network,

( 0 (R( k l r) I shall now describe the mode of operation of theresistance network of the present invention. I will assume, as shown inthe drawing, that the arms 0 and P respectively engage the contacts Reand Rb, the arm Q engages the contact It's and that it is desired todecrease the output voltage E0. First, the arm Q is moved through R'ctoward R'o. The result is a progressive decrease in said output voltage.Assuming that the arm Q has reached the contact Ro and it is desired tofurther reduce the output, the arms 0 and P are moved toward the contactR0 in such a manner that the arm 0 is engaged with the contact Rb beforethe arm P is disengaged therefrom. This movement is continued until tharm P is disengaged. At this time the arm Q is moved so as to engage thecontact Rm and the arm P is moved into engagement with the contact Ra.During all of these movements the arm 0 remains engaged with the contactRb and no change occurs in the output voltage E0. Now the arm Q can bemoved toward R'o as previously described in order to decrease the outputvoltage E0. The entire procedure outlined can be continued until thedesired reduction in the output has been attained.

To increase the output voltage E0 all of the foregoing movements arereversed.

This completes the description of the present invention and it will benoted that I have provided a simple resistance network whereby a voltagedrop can be varied substantially smoothly and continuously so as toclosely approximate a nonlinear mathematical curve, such as theexponential curve of a charging capacitance.

Other objects and advantages of the present invention will readily occurto those skilled in the art to which the same relates.

I claim:

1. In a resistance network, a first group of resistors each having avalue such that the total resistance of selected combinations thereof isa given non-linear function of the number of resistors comprising eachsuch combination, and a second group of resistors each havin a valuesuch that the equivalent resistance of a parallel combination ofselected resistors of said second group and any selected resistor ofsaid first group i an approximately linear function of the number ofresistors of said second group entering into said parallel combination.

2. In a resistance network, a first group of resistors each having avalue such that the total resistance of selected combinations thereof isan exponential function of the number of resistors comprising each suchcombination, and a second group of resistors each having a value suchthat the equivalent resistance of a parallel combination of selectedresistors of said second group and any selected resistor of said firstgroup is an approximately linear function of the number of resistors ofsaid second group entering into said parallel combination.

3. In a resistance network, a first group of resistors each having avalue such that the total resistance of selected combinations thereof isa given non-linear function of the number of resistors comprising eachsuch combination, and a second group of resistors connected in serieseach of whose value is given by the expression Where E is the averagevalue of the resistors of said first group, n is the number of resistorin saidsecond group, and h is the number of the resistor of said secondgroup whose value is being determined.

4.111 a resistance network, a first group of resistors each having avalue such that the total resistance of selected combinations thereof isan exponential function of the number of resistors comprising each suchcombination, and a second group of resistors connected in series each ofwhose value is given by the expression Rn (n-h)(nh+1) where R is theaverage value of the resistors of said first group, n is the number ofresistors in said second group, and h is the number of the resistor ofsaid second group whose value is being determined.

5. In a resistance network, a first group of series-connected resistorseach of whose value is given by the expression where A, B, and Rs areconstants of the network, 11 is the number of resistors in said firstgroup, and k is the number of the resistor whose value is beingdetermined, and a second group of resistors connected in series each ofwhose value is given by the expression Rn (n-h) (nh+1) where R is theaverage value of the resistors of said first group, n is the number ofresistors in said second group, and h is the number of the resistor ofsaid second being determined.

group whose value is 1,479,051

6 6. In a resistance network, a first group of series-connectedresistors each of whose value is given by the expression k-l 1e where A,B, and Rs are constants of the network. n is the number of resistors insaid first group, and la is the number of the resistor whose value isbeing determined, a second group of resistors connected in series eachof whose value is given by the expression REFERENCES CITED The followingreferences are of record in the file of this patent:

UNITED STATES PATENTS Number Name Date Best Jan. 1, 1924 1,948,675Rhodes Feb. 27, 1934

